A PhD is only as good as the reputation of your advisor. If everybody knows your advisor then you won't have a problem finding a job in academia.

I would amend this to be "if everybody knows your advisor you'll have FEWER problems finding a job in academia." Some fields are very, very crowded (theoretical physics, for instance). For a very brief time, I was in a small team at a consulting company where 3 out of the 4 of us had done a science phd under a Nobel winner, and still ended up making major career transitions after half a decade of postdocs. Science is crowded, the more basic the research the more crowded the field. To first order, no one gets a job. If you are under a famous advisor you might move your odds up to 1/10 or 1/5 or something like that.